Abstract:
The long-period modes of a differentially rotating, solar-type star are consided. Two modes are found. The non-axisymmetric modes are Rossby waves, also known as r-modes, with the Coriolis force as the dominant restoring force.These oscillations have periods of order a month to a few years for solar parameters. An axisymmetric mode with purely magnetic restoring force is also found, which we call the b-mode. The fundamental period of the b-mode is large, of order 300 years. Higher harmonics are shown to have period of order 10-20 years. The dispersion relation for depends on the variation of the magnetic field strength and the mass density with depth through the convection zone. We suggest that if these modes could be observed information on the structure of the magnetic field below the surface could be deduced. Accounting for differential rotation does not affect the period of either mode, however the radial and lattitudinal profiles of the wave amplitude are slightly modified when compared with the previous solutions assuming solid body rotation.
